Harvard researchers use math to find smarter ways to defeat cancer

It’s become an increasingly common pattern in cancer treatment: a drug targeted to the specific genetic mutation that drives a cancer has an astonishing result, melting the tumor away. Months later, the cancer begins to grow back. Patients move on to the next drug—if there is one. The pattern may repeat, but all too often, cancers return and doctors and patients find themselves out of effective treatments.

Now, a new study authored by an unusual combination of Harvard mathematicians and oncologists from leading cancer centers uses modeling to predict how tumors mutate to foil the onslaught of targeted drugs. The study, published Tuesday in the journal, eLife, suggests that administering targeted medications one at a time may actually insure that the disease will not be cured. Instead, the study suggests that drugs should be given in combination.

If proven correct, the model could help guide the design of clinical trials, giving physicians and researchers powerful clues about which combinations of drugs should be given, and in what combinations. The researchers are now collaborating with biologists to verify their model in tests in laboratory dishes and animal tests.

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“We want to actually predict, without the extensive clinical trials ... which combinations might be effective,” said Ivana Bozic, a post-doctoral researcher at Harvard who led the work. “The main conclusion we have is that single treatment will almost certainly fail in solid tumors, and if you give drugs sequentially ... then it’s going to fail. Basically, the way to go forward is to combine these two drugs.”

The researchers started with 20 patients with melanoma who responded to a drug that targeted a mutated gene called BRAF. By looking at the variety of responses in those 20 patients, they built a mathematical model of how the cancer mutated to escape the drug. Then, they applied their model to several kinds of cancer.

Since they were using models, not particular drugs and real patients, they weren’t able to say which drugs to give in what combinations, but instead to get a general picture of what kind of pharmaceutical firepower they would need to be effective against pancreatic cancer, colon cancer, and metastatic melanoma. They found that in almost no cases would one drug work, but that using two drugs in tandem could result in long-term control of cancer. In patients with advanced cancers, they found three drugs would be needed.

The study also showed the pitfalls of drugs that are too similar. Many cancer drugs try to attack the same targets, which can lead to multiple effective therapies. But combinations of drugs will only work if the cancer’s way of eluding the drugs is different. If the tumor would effectively using the same escape hatch by developing an identical mutation, the drug combination won’t work.

All models have their faults, and the researchers will have to show theirs is truly predictive before it will be useful. But tools that allow doctors to design clinical trials more likely to work could speed up the development of useful therapies.

“It seems, for historic reasons, drugs are given sequentially and sometimes there’s an issue of side effects,” Bozic said. “However, I would like to make parallels with HIV, where also when a single drug, AZT, was the norm for treatment, most patients were failing treatment.”

When patients started getting combination therapies, however, a once fatal disease was transformed into a chronic condition.